Question

Find the value of  `cot^-1(1) + sin^-1 (- sqrt(3)/2) - sec^-1 (- sqrt(2))`

Answer 1

x = `cot^-1(1)`

y = `sin^-1(- sqrt(3)/2)`

cot x = 1 = `cot  pi/4`

sin y = `- sqrt(3)/2 = sin (- pi/3)`

x = `pi/4`

y = `- pi/3`

z = `sec^-1 (- sqrt(2))`

sec z = `- sqrt(2)`

sec z = `- sec  pi/4`

= `sec(pi - pi/4)`

= `sec  (3pi)/4`

z = `+  (3pi)/4`

`cot1(1) + sn-1(- sqrt(3)/2) - sec^-1(- sqrt(2))`

= `pi/4 - pi/3 - (3pi)/4`

= `- pi/3 - (2pi)/4`

= `- pi/3 - pi/2`

= `- (5pi)/6`